The government has given its strongest indication yet that it may back down over plans to hold the forthcoming Iraq inquiry in secret.

Ministerial sources indicated that Gordon Brown is preparing to accept parts of a Conservative motion to be debated on Wednesday that the inquiry "should be wherever possible be held in public".

Jack Straw, the justice secretary, said yesterday that he would be prepared to give most of his evidence to the inquiry in public.

The prime minister announced last week that the inquiry would be held in private but was later forced to open up the terms of the inquiry after pressure from a broad coalition of former generals, former prime minister John Major and peers from all parties.

Brown told Sir John Chilcot, the former civil servant charged with heading up the independent five-strong inquiry team of privy counsellors, that if he wished he could hold the sessions with the families of those who died in service in public.

Now, under renewed pressure from the Tories – who have also changed position from originally backing a private inquiry to demanding a largely public inquiry – the government is planning to concede more ground.

However, it will stop short of backing Tory calls for the terms of reference to be widened.

The partial government climbdown comes as it emerged that the prime minister was poised to appoint a leading Conservative with experience of the first Iraq war to the inquiry.

Lynda Chalker, deputy foreign secretary under John Major, was put up privately by David Cameron, who is now complaining in a parliamentary motion that the membership of the inquiry "should be wider and more diverse than the government has proposed".

Chalker declined to take up the post because, as chairman of Africa Matters, a charity supporting African redevelopment, she says she has not got the time. So Cameron had to withdraw her name.

Chalker yesterday confirmed the approach. William Hague, the shadow foreign secretary, blamed the government for giving the Tories "just 48 hours notice" to come up with someone to serve on the inquiry.

But a Downing Street source denied this, saying it showed that Cameron was being "disingenuous and opportunistic" by attacking Brown for not including a diverse membership and then not being able to appoint anyone to sit on it.

Meanwhile, Straw told the BBC1 Andrew Marr show that he would be prepared to give most of his evidence in public. He was foreign secretary at the time of the 2003 invasion of Iraq.

The prime minister had taken the Franks Inquiry into the Falklands war, which was held in private, as a model, he said. "That was what the Conservatives had been calling for time after time after time, and they dismissed other inquiries that had been held," he said. "Now, Franks was held in private exclusively. It was for that reason, no other, that Gordon Brown decided to do that."

Straw added: "As foreign secretary at the time I have no problem with giving most of the evidence I have got to give in public."

Later Sadiq Khan, transport minister, Britain's most senior Muslim politician, told BBC1's Politics Show: "I suspect there will be many, many parts of the inquiry held in public."

Asked to admit that the situation "did not look good", Khan conceded: "It looked awful. One of the reasons was a lack of understanding of what chairs of inquiries do."

He added: "The terms of reference were set out, from 2001 to 2009, Sir John will decide how his inquiry is held."

One reason why Brown is thought to have agreed to a private inquiry may have been pressure from the former prime minister, Tony Blair.

The Observer reported that Blair pressed Brown to hold an inquiry behind closed doors because he feared he would be subjected to a "show trial" if it were open to the public.

He is said to have communicated his view via the cabinet secretary, Sir Gus O'Donnell. He feared that a direct conversation would be leaked, The Observer claimed.

A spokesman for Blair said: "This is a decision for the current prime minister, not the former one."

He is thought to be have been backed by O'Donnell. The Northern Ireland secretary, Shaun Woodward, confirmed that Blair had held talks with O'Donnell about giving evidence to the inquiry.

He said: "Of course the cabinet secretary discussed this with the former prime minister because he obviously will be one of the major witnesses who will be giving evidence to Sir John Chilcot's inquiry."

The Liberal Democrat leader, Nick Clegg, said Blair should give evidence to the inquiry in public and under oath.

He said he would be meeting Chilcot this week to tell him the only way for the inquiry to have legitimacy is for it to be as public as possible.